Question

Is the Laplace transform of e^(at+b) (e^b)/(s-a), or (e^bs)/(s-a)? Wolfram alpha gives the first, but an example in Paul's online notes gives the second.

Answer 1

\[L \left\{ e^{at+b} \right\}=L \left\{ e^{at}e^b \right\}=e^bL \left\{ e^{at} \right\}=\frac{ e^b }{ s-a }\]. maybe you should check the notes again.

Answer 2

Okay thanks. It was in the example at this link http://tutorial.math.lamar.edu/Classes/DE/HOLaplaceTransforms.aspx

Answer 3

the note is also right. \[L \left\{ 3u_6(t)e^{-5(t-6)} \right\}\] has one factor the Heaviside function \[u_6(t)\]

Answer 4

Oh, I see. Thanks